Less is More: Similarity of Time Series under Linear Transformations

Abstract

When comparing time series, z-normalization preprocessing and dynamic time warping (DTW) distance became almost standard procedure. This paper makes a point against carelessly using this setup by discussing implications and alternatives. A (conceptually) simpler distance measure is proposed that allows for a linear transformation of amplitude and time only, but is also open for other normalizations (unachievable by z-normalization preprocessing). Lower bounding techniques are presented for this measure that apply directly to raw series.